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Elenna [48]
3 years ago
12

The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel st

raight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the actual track (the shaded region).

Mathematics
1 answer:
Nostrana [21]3 years ago
3 0
First we calculate the area of each semicircle (half the area of the full circle)
and we substract them to get the area of the curved shaded part

1/2 * [ pi * (80/2)**2 ] - 1/2 * [ pi * (60/2)**2 ] = (800-450)pi = 350*pi m2

the area of the full circle   (both sides) ------------2*350*pi m2--750*pi m2

The area of the straight line = 2 * (100 *10) = 2000 m2

Total Area = 2000 +700*pi m2 = 4198 m2
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3 years ago
Two numbers whose sum is 44 and whose product is a maximum
Mashcka [7]

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x)                    Remove the brackets

Max = 44x - x^2                   Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x )               Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done  is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

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If it is not zero it will be minus and that will subtract from 484

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xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.


4 0
3 years ago
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